However it does not seem that the proposers of the quantum SWITCH ever meant to claim that this experiment represents a superposition of different causal structures in the sense in which MacLean et al use this term. Rather they argued that it demonstrates a superposition of different causal orders[1]}. In fact there is some confusion here because the language used by researchers in this programme equivocates between `causal order,' `causal structure' and `causal relations.' In some cases it seems to be implied that all three are the same: for example ref [2]} seems to be making an identification between `causal order' and `causal relations' in their reference to `realization of indefinite causal order (ICO), a theoretical possibility that even causal relations between physical events can be subjected to quantum superposition.' But on further examination, it is clear that these things are not identical. The term `causal relations' is naturally understood as referring to `cause-effect relations' of the kind that we are familiar with from our macroscopic experiences, and the term `causal structure,' usually seems to refer to causal structures as analysed in the causal modelling framework, i.e. structures made up out of these `cause-effect relations.' Causal order, on the other hand, does not invariably refer to cause-effect relations. The quantum SWITCH is a good example: for after all, even if we ignore the control qubit it is clearly not the case that in one branch \(A\)  causes \(B\)  and in the other \(B\)  causes \(A\)  - the experiment is not set up in such a way that the application of the first gate is `the cause' of the application of the second gate. But nonetheless the order in which these events occur is meaningful, otherwise the two branches would be identical and we would not have a superposition at all. And moreover, we have seen that there are indeed good reasons to think that it really is the order of events which differs between these branches in significant ways. So it seems reasonable to say that these events stand in a physically meaningful causal order even though they do not bear any cause-effect relation to one another.
